An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig. 12.16), each piece measuring $ 20 \mathrm{~cm}, 50 \mathrm{~cm} $ and $ 50 \mathrm{~cm} $. How much cloth of each colour is required for the umbrella?
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Given:

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours, each piece measuring \( 20 \mathrm{~cm}, 50 \mathrm{~cm} \) and \( 50 \mathrm{~cm} \).

To do:

We have to find the cloth of each colour required for the umbrella.

Solution:

Let the side of each triangular piece of cloth be $a=20\ cm, b=50\ cm$ and $c=50\ cm$.

Therefore,

Using Heron's formula,

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Since,

$S=\frac{a+b+c}{2}$

$S=\frac{20\ cm+50\ cm+50\ cm}{2}$

$S=\frac{120\ cm}{2}$

$S=60\ cm$

This implies,

$A=\sqrt{60(60-50)(60-50)(60-20)}$

$A=\sqrt{60(10)(10)(40)}$

$A=200\sqrt{6}\ cm^2$

Therefore,

The area of the cloth of each colour required for the umbrella $=5\times 200\sqrt{6}\ cm^2$

$=1000\sqrt{6}\ cm^2$.

Hence, the area of the cloth of each colour required for the umbrella is $1000\sqrt{6}\ cm^2$.

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Updated on: 10-Oct-2022

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